Actually Varian, I think I figured out why you are getting this wrong. The increase in probability does in fact have DR which is what I think you are trying to say. That doesn't actually matter though because what we are really interested in is the expected value of your attack.

Originally Posted by Squirl

I suppose "prove" would have been a better word. Probabilities, man. They're the least intuitive math concept for me, but I suppose I "explained" it as well as I can.

Also, your explanation is simply a statement. It doesn't explain anything. I tried my best, but if the people in this thread don't get it, they will just have to trust us.

Please show me your expected value calculations for a 1000 damage attack at different crit levels. You will see why you are wrong if you do.

Again, your example fails. OMFG yes crit is more valuable if your non crit damage is higher. Obviously the rogue with the higher base hit gets a larger gain. You can't compare those two as you changed other things around. All your example can ever show is that crit increases in value as other factors increase your damage.

Ok, but the part you are missing is that when the devs design us, one thing they do (besides apparently a fuck ton of peyote) is to take into account the actual damage output, and balance around that. The first rogue there, with the larger base damage, is that way because he doesn't have the crit to help him out. The second rogue has the base crit, so they need to reduce the raw damage he does so he has the same outcome as the first rogue.

Which of these assertions are you having a hard time getting the math behind?

1)- Having a large base crit- on a move, or in general- will reduce the value of critical strike rating for you, versus if you did not have that base crit.
2)- If you have a large amount of rating- say, 15,000 haste rating at level 90- and you are given the choice between 1,000 crit rating and 1,000 more haste rating, choosing the rating you have less of (in this case crit rating) will give you more damage.
3)- At any set of gearing and stats, each rating has a value that is commensurate to the amount of average damage it will add. Every point of an uncapped (or effectively uncapped) rating that you add changes the values of the other ratings, normally increasing them.
4)- Stats that stack additively will increase dps at a slower rate than stats that stack multiplicatively.*

*A base crit of +30% on backstab, as we had from talents, would add to your rogue's +15% crit to crit 45% of the time. But say 40% haste would stack with slice and dice to be, not 80% faster, but 1.4*1.4=19.6 = 96% faster. (4) isn't really important to this, but you did bring it up.

Ok, but the part you are missing is that when the devs design us, one thing they do (besides apparently a fuck ton of peyote) is to take into account the actual damage output, and balance around that. The first rogue there, with the larger base damage, is that way because he doesn't have the crit to help him out. The second rogue has the base crit, so they need to reduce the raw damage he does so he has the same outcome as the first rogue.

Which of these assertions are you having a hard time getting the math behind?

1)- Having a large base crit- on a move, or in general- will reduce the value of critical strike rating for you, versus if you did not have that base crit.
2)- If you have a large amount of rating- say, 15,000 haste rating at level 90- and you are given the choice between 1,000 crit rating and 1,000 more haste rating, choosing the rating you have less of (in this case crit rating) will give you more damage.
3)- At any set of gearing and stats, each rating has a value that is commensurate to the amount of average damage it will add. Every point of an uncapped (or effectively uncapped) rating that you add changes the values of the other ratings, normally increasing them.
4)- Stats that stack additively will increase dps at a slower rate than stats that stack multiplicatively.

None of them. Are you following my expected value numbers? Doesn't seem like you understand the math behind EV....

1.) False. I already showed that expected value of a hit per 1% change in crit chance is identical with my EV calculation earlier at 98, 99, and 100% chances.
2.) Irrelevant. Has to do with co-scaling of stats.
3.) Yes, but irrelevant. Not talking about co-scaling of stats.
4.) Irrelevant. Multiplicative stats aren't in question here (crit).

Like I said to him, show me your math. What is your expected value calculation for a hit of 1000 damage?

Please show me your expected value calculations for a 1000 damage attack at different crit levels. You will see why you are wrong if you do.

Looking at a single attack will produce what you expect. The point is that probabilities act funny when you look at multiple events of which the outcomes of each do not affect the outcomes of others. You can see this in drop chances very easily.

There's a 1% chance that a mount will drop each time you kill a boss. Looking at each individual time you kill the boss, the drop chance is 1%. Looking at 100 events where you killed the boss, the drop chance is not 100% and it's not 1% either. I forgot the exact maths, but the chance that it will have dropped once in those 100 kills can be calculated and that value fluctuates based on the chance that it will drop in a sole event. Altering the drop chance does not have the effect on the 100 event set that you would expect. That is, if the drop chance in a sole event is higher, the chance that it will drop once in that 100 event set does not go up at a linear rate.

The point is that probabilities act funny when you look at multiple events of which the outcomes of each do not affect the outcomes of others. You can see this in drop chances very easily.

There's a 1% chance that a mount will drop each time you kill a boss. Looking at each individual time you kill the boss, the drop chance is 1%. Looking at 100 events where you killed the boss, the drop chance is not 100% and it's not 1% either. I forgot the exact maths, but the chance that it will have dropped once in those 100 kills can be calculated and that value fluctuates based on the chance that it will drop in a sole event. Altering the drop chance does not have the effect on the 100 event set that you would expect.

Like I said, I already explained it as best as I can.

Sorry, that doesn't apply. I think you need to go back to your statistics book... Why do they look funny? It is just a case of independent events and expected value works just fine there. Expected value is the probability of each event multiplied by the event's value. As you repeat the independent events enough times so that the number approaches infinity, the average of the results will be the expected value.

Drops are different in that you aren't looking at the EV of the drop itself but the expected number of attempts to get the drop.. In fact most people get confused because they don't realize it is independent. Like how in your example lots of people tend to think that since they previously did it 99 times, the chance of getting it next time is higher when it is in fact still 1% (independent events). The probability of not getting a single mount in 100 runs with a 1% drop is ~36.6%. Thats not particularly relevant to this though... The probability of getting at least one is ~63.3%. If you forgot the math, why are you weighing in on this at all?

Edit: Ok let me go into this further to show you why it doesn't matter. Lets say your 1% mount's value is 1 for simplicity. Whats the expected value of you running the place one time? It is .01. Increase the drop rate to 2%, then the EV is .02. At a 2% drop rate, the chance that you run it 100 times and get no mounts is ~13.3%. Why isn't that what you would expect? It should be. The change in EV per chance in % drop rate is going to be constant just like it is with crit chance. The change in the chance of you getting 0 mounts in 100 runs per drop rate will not be constant, but where you guys are messing up is that has no impact on the expected value.

Sorry, that doesn't apply. I think you need to go back to your statistics book... Why do they look funny? It is just a case of independent events and expected value works just fine there. Expected value is the probability of each event multiplied by the event's value. As you repeat the independent events enough times so that the number approaches infinity, the average of the results will be the expected value.

Drops are different in that you aren't looking at the EV of the drop itself but the expected number of attempts to get the drop.. In fact most people get confused because they don't realize it is independent. Like how in your example lots of people tend to think that since they previously did it 99 times, the chance of getting it next time is higher when it is in fact still 1% (independent events). The probability of not getting a single mount in 100 runs with a 1% drop is ~36.6%. Thats not particularly relevant to this though... The probability of getting at least one is ~63.3%. If you forgot the math, why are you weighing in on this at all?

Because there was a conversation on EJ years ago about crit when it was actually possible for us to cap crit. Crit gets worse the more you have relative to AP. That is, its EP goes down. That's what everyone in this thread has been saying.

I guess that drop example was not entirely relevant. I might be posting from work and not really focused...

Because there was a conversation on EJ years ago about crit when it was actually possible for us to cap crit. Crit gets worse the more you have relative to AP. That is, its EP goes down. That's what everyone in this thread has been saying.

I guess that drop example was not entirely relevant. I might be posting from work and not really focused...

Again, irrelevant. Stop side tracking the argument with co-scaling of stats. It is retarded and causing this to get no where. The question was whether built in crit made crit less valuable. Don't go adding in more ap or weapon damage or what not. Crit itself doesn't provide a smaller increase in EV the more you add (unless you are capped) which means 15% crit on mut didn't lower the value of crit. What it did do was increase the value of other stats because of how they scale together.

Think of it like a foreign exchange market. I have a $1. The euro goes up compared to the dollar, so yeah if I convert my dollar into euros (EP) it went down. However my $1 is still worth $1 so the actual value is still the same.

Edit: Ok that might not be the best example unless you also assume that the price of goods stayed constant so the actual purchasing power of the dollar is the same...

Again, irrelevant. Stop side tracking the argument with co-scaling of stats. It is retarded and causing this to get no where. The question was whether built in crit made crit less valuable. Don't go adding in more ap or weapon damage or what not. Crit itself doesn't provide a smaller increase in EV the more you add (unless you are capped) which means 15% crit on mut didn't lower the value of crit. What it did do was increase the value of other stats because of how they scale together.

Think of it like a foreign exchange market. I have a $1. The euro goes up compared to the dollar, so yeah if I convert my dollar into euros (EP) it went down. However my $1 is still worth $1 so the actual value is still the same.

You're going to have to define "value", then. Most of us go by EP, which is weighted against AP. 1 EP = 1 AP. All of our stats scale together.

You're going to have to define "value", then. Most of us go by EP, which is weighted against AP. 1 EP = 1 AP. All of our stats scale together.

Why? I already defined it for you. Expected value... its one of the most basic statistics so if you know any probability you should know what it means. What is EP used for though? Its a metric to make it clear which will give you the highest expected value for damage done. The value isn't the EP itself.

Edit: Though if you meant my example you're right, I needed to add in some stuff about purchasing power which makes it kind of a bad example.

One guaranteed crit every 3min does NOT make rogues not care about crit.

What makes rogues care about crit are class mechanics that interact significantly with crits. 1% crit chance is 1% extra damage, and the amount of crit rating it takes to get 1% crit is twice as much as it takes to get 1% haste, hit, etc.

What makes rogues care about crit are things like seal fate (it needs to grant more combo points, say add finishers to its effect) to make assassination value crit. Focused attacks in wrath made crit very desirable for assassination (and if they tied energy regen to crits like this I assure you crit would become a very good stat for them).

Old prey on the weak made combat rogues care about crit. The wrath version of sinister strike glyph also achieved this.

Backstab glyph made sub rogues care about crit. HaT does too, but in a raid where you get HaT procs every 2 sec, sub starts to value crit less.

If they want rogues to desire crit, then need to make our crits do SOMETHING other than give us double damage once.

A lot of the math in here is REALLY overthinking the situation. AT EQUAL DPS, with ALL OTHER STATS EQUAL, crit is worth less the more you have (as per the 1.00-1.10 and 1.9-2.0 discussion) however~ that assumes you've set your priorities differently, and not that all your gear and DPS has scaled accordingly. The PERCENTILE gain may diminish, but if you're at 1,000 DPS and gain 10% crit, you're at 1,100 DPS. If you're at 1,100 DPS with 10% crit and gain 10% crit, you're at 1,200 DPS (DISCOUNT SEAL FATE, PLEASE). The percentile gain diminishes, but the numeric gain is linear, until caps or with influxes of more complex additions like the interaction of SF and mutilate vs. combo point gen.

The same is true in mastery and in haste. The percentile gain for the same rating gain lowers as you get more, but the linear gain (on auto-attacks) will remain steady. If SnD stacks with haste and you go from 0% to 10%, your AA goes from 140% to 154%. Get another 10% and it goes from 154% to 168%. You've gained 14% attack speed both times! The first was a relative gain of 10%, but the second was only a relative gain of 9.09~%. Etc. with mastery...

Which leaves the reason we still don't like crit at: mastery and haste are just better under the current design. If combo points mattered a LOT more for assassination, crit would eventually come ahead.

Edit: Oh right the point about passive crit: The more passive crit we have, the less likely crit is to much up with the above system, because we'll be operating at a linear gain, but with a percentile increased base crit chance (and +crit from agi!) which serves to give it "diminishing returns" not linearly, but with respect to other stats. If you're picking between a 10% crit boost and a 10% haste boost (assuming 1% haste and 1% crit, at values of 0, are 1% damage each) you want to pick the one you have less of. It's the basic lineup for causing stats to influence other stats. At 1000 DPS, 0 haste, 0 crit, 10% haste and crit are both worth 100 DPS. At 1000 DPS, 0 haste, 60% crit (cata ambush value), 10% haste is worth 100 DPS. 10% crit is worth 62.5 DPS, and is less impressive.

Edit 2: I was going to continue the example. Having gained 10% crit in the 0/0 example, you're now at 1100 DPS, 0 haste, and 10% crit. Gaining another 10% crit puts you at 1,200 DPS, but gaining 10% haste puts you at 1,210. The crit retains it's 100 DPS value, but the haste's value went from 100 to 110 DPS because of the increase in crit.

Outside the math: the warrior discussion and Shadowboy's points ^^ have a lot more to do with why our crit is friggin' boring.

A lot of the math in here is REALLY overthinking the situation. AT EQUAL DPS, with ALL OTHER STATS EQUAL, crit is worth less the more you have (as per the 1.00-1.10 and 1.9-2.0 discussion) however~ that assumes you've set your priorities differently, and not that all your gear and DPS has scaled accordingly. The PERCENTILE gain may diminish, but if you're at 1,000 DPS and gain 10% crit, you're at 1,100 DPS. If you're at 1,100 DPS with 10% crit and gain 10% crit, you're at 1,200 DPS (DISCOUNT SEAL FATE, PLEASE). The percentile gain diminishes, but the numeric gain is linear, until caps or with influxes of more complex additions like the interaction of SF and mutilate vs. combo point gen.

Um you just, like I did, showed that crit is NOT worth less the more you have. As you said at the end of that, the gain is linear. The percentile gain may be less, but that doesn't mean crit is worth less in absolute terms which is what matters because you the game is counting in actual damage. So again, having baseline crit doesn't make crit less valuable barring caps.

Also to be fair, if you really want to use percents you need to use them the whole way and not stop and do things additively. If you have 0% crit and to go 10% that is a 10% dps increase and a 10% crit increase. If you further increase by 10% you have 121% crit, which i know sounds wierd but you were actually at 110% after the first 10% crit, and you just got a (121-110)/110 % dps increase... which just so happens to be 10%. The only reason this "breaks" and people think it is having DR is if you are adding a percent instead of increasing by a percent.

Edit: Err in that last part I should perhaps say effective crit bonus rather than 10%. But anyway the point is that if you actually scale it by a %, you get the same linear returns in % gain you do with actual damage gain.

But you ARE adding a percent chance to crit, unless you've found a way to increase your incoming crit rating on gear because of the crit you already have =). I'm not saying people in the thread were wrong, but that the primary argument (linear/regressive) are two sides of the same coin (value/percentile). Getting 10% damage-from-crit with respect to your 10% existing crit would in fact require 11% more crit, but that's not the option we've been talking about.

Beyond that, at any given point in DPS, you gain more from the stat you have less of (see the second/third portions of my post) which makes base crit % devalue crit gain, because we're NOT starting at 0, and the gains are NOT multiplicative. If you have +60% crit to ambush and 10% chance to crit, your ambush crits 70% of the time, not 76% of the time. If you add 10% crit to your ambushes, you've gained 6.25% damage. If you gain 10% more ambushes, you've gained 10% more damage (which would assume 0 haste before adding 10%, no CP/energy interaction etc. and this example doesn't work in a vacuum but it's the best I could do atm). If we're talking about being at the same starting DPS, you'll always scale fastest with the lowest multiplier (crit X haste X mastery, as if they were 1% gains).

Which of course explains how getting a lot of 1 stat raises the value of other stats with respect to it blah blah blah. Crit still sucks because outside SF it doesn't do any "complex" interactions with our lineup, and at a stat-rating-to-effect ratio it's lower than the other stats. It's further "devalued" by the anti-ratio scaling provided by agi. Crit still has linear gain, but value from haste and mastery has been increased by the crit you get from agi, while crit rating is NOT increased by the crit you get from agi.

You are adding a % of crit, but your real gain is the damage itself which as you said is linear.

And you are right, thats what I was trying to say though. If you were to scale by a percent instead of add, it will also be linear gains. The problem is only when you add by a percent and then look at percent gain. You're right that wasn't what was being talked about, I was just adding that you can still use percents and end up with it being linear. Probably only derailed things by bringing that up, so dropping it now.

Anyway like you said in that last paragraph. Crit has a linear gain. Starting with 15% built in crit from talents like we use to on mutilate never made any difference in the damage gain from another 1% crit. It only effected the relative values of other stats through how they co-scale which was the original point anyway. Crit doesn't devalue crit. More crit increases the relative value of other stats but leaves crit as it was.

You later agree it is linear which means that is not possible. Starting with 15% from talents and adding 1% crit will give you the exact same expected value for your hit of say 1000 as having 15% crit rating from gear and adding another 1% crit. There is no difference because unlike haste, crit values from different sources are added. The % gain may be decreasing but in this example you are gaining a constant 10 damage to your expected hit for each 1% crit you add meaning the value is 10 damage. It is still 10 damage going from 99% to 100%.

Think of it as money. $10 buys $10 worth of stuff even if you have $100 in your bank or $1M in your bank. The value of that $10 is not somehow decreased because you have $1M in your bank account. Now you could bring up something like "relative to your net worth." Well how about I define my utility function in such a way that it increases exponentially as the % of total hits that crit increases and then tell you that more crit increases the value of crit exponentially the more of it you get until you cap? That could be true, relative to my utility gain, who cares. Key word being "relative." The only important thing is that I in fact gained 10 damage not relative to any outside conditions no matter what my % crit was at before adding the next 1%. (To be clear, I'm using "utility" in the economics sense).

Devalues, with respect to other stats. The DPS gain per crit may remain the same, but the increase in value of other stats as a result of base crit necessarily makes crit less important by comparison.

There isn't a way to fit the bank analogy to this, but we have to see crit both in a vacuum and in relation to other stats. The gain IS linear, but it increases the gain from other stats as a result, as per the volume of an object (LxWxH) we're using CritxHastexMastery, and when one value has increased, the others become a greater gain by comparison. Crit RATING is devalued because we have Crit (Crit Rating + Crit from Agi) X (Haste Rating X haste multipliers) X (Mastery score). Since there are 2 "feeders" into our crit value in the CritxHastexMastery model, we'll need less of the crit rating feeder to match the level of crit needed for maximum increase in the above model. If the same rating is needed to get 1% damage from crit, haste, or mastery. Which of course isn't the case in the first place, pushing our stat weights further off 1:1:1.

Yes but saying it "devalues" and "devalues wrt" are not the same thing. The real gain is constant.

And I don't see how the bank analogy doesn't work (unlike my last failed one). Say gas price goes up, your $10 is now worth less relative to a gallon of gas, but you would never say that your $10 actually has less value (other things constant). Or what if gas goes up and say the price of a burger goes down (ok usually food goes up but I whatever). Did your dollar go up in value? Down in value? No one thinks that way because the dollar has a specific value independent of those things.

This whole "relative to" thing is completely retarded anyway. I already gave you an example of meaning "relative to a personal utility function" which can be pretty much anything. If you want to set some conditions on something you need to say them. Saying crit devalues with more crit is flat out wrong, there is no room for discussion, it is linear, there is no DR, you seem to agree on this. Yeah you can twist it however you want by adding in the words "relative to X" but those weren't there and need to be stated. The second you start throwing in "relative to X" you have to then consider changes in X because in all the cases here, the X isn't a constant, and in most cases that isn't worth doing. You don't usually want to go in adding additional variables to something you are analyzing if you don't have to... why do you want to do it here? You can easily analyze the actual gain of 1% crit without additional variables... why would you want to not only add in those additional variables (in this case the other stats you mention) when there is already a perfectly standard point of reference (the actual damage) and on top of that state your results without mentioning any of those variables by saying crit devalues more crit... The standard of comparison in this case boils down to damage which is linear in gains. The values of those other stats you mention are all obtained through calculations from the actual damage which is the end result. The percent gain you mention is derived from the damage numbers you actually dealt, and the value of haste/mastery you mention is based on the damage they will add. Now you aren't "wrong" that the percent gain has DR or that the relative gain compared to other stats gets smaller, but neither of those are what was originally said and are just adding on extra 'stuff' to the results...

Crit rating isn't devalued just like any other sources. Until you cap, 1% crit from agi or 1% crit from rating or 1% crit from a talent all function identically and provide the same return, therefore your "feeders" idea doesn't really work. Neither the original comment nor what I was saying was about reaching an optimal amount of crit to maximize your dps (which yes you should be doing, obviously don't just stack crit until cap because the damage gains are constant). If it was, your feeders concept would certainly be applicable. Using your formulas and holding non crit values constant:
(15% Crit Rating + 0% Crit from Agi) X (Haste Rating X haste multipliers) X (Mastery score)
= (0% Crit Rating + 15% Crit from Agi) X (Haste Rating X haste multipliers) X (Mastery score)

The only way you are not getting it to be the same constant damage gain is if you are looking at the damage result with respect to something else which itself isn't a constant gain (such as the relationship between the stats).

If you are doing the valuation of something, you would never just skip over the absolute value and state your results in relative value (especially without saying relative to what). I can't understand why people are so eager to do so in this case.

So, you just want us to say other stats get better the more crit you have rather than crit gets worse the more you have.

Well the first point is right, but its kinda trivial. All the stats are positively correlated. Its not like at some point for stat X increasing stat Y (not counting choosing Y over Z, but just say the difference in adding a gem of stat Y into a pris socket) can cause a dps loss.

The latter is just wrong. Worse the more you have means the slope is concave down at that point (probably asymptoticly approaching some number rather than getting to a point and becoming negative). As shown, the real gain has a constant slope.

As for what I want... how about people saying what they mean and getting it right? Also not using math based on 2 different underlying conditions to try to prove something (as was the first example) or introducing a bunch of cointegrated variables and then people to actually give their math instead of just stating stuff and saying stuff like "i know the math but..." I showed pretty early on that the expected value of your attack increased linearly with crit, I "wanted" to see what they were calculating that showed the increase in EV was not linear (aside from Muga, he did provide his, my dispute with him was simply that he was adding in words to be able to get the other conclusion).

Anyway, the better way to say it so it isn't an obviously trivial case would probably be that crit has decreasing marginal returns {the return being [v(1)-v(0)]/v(0)} which is true even though the actual value (other things constant) is the same until cap.

Cold Blooded was the worst cd in game and I am thrilled to see it gone. Right now according to shadowcraft crit is actually beating expertise to point and easily beating haste. Assasination does need another cd but please dear god not cold blooded. I would rather have hunger for blood back than that.